Fault-tolerance of the [[8,1,3]] non-CSS code

We present a fault-tolerant [[8, 1, 3]] non-CSS quantum error correcting code and study its logical error rates. We choose the unitary encoding procedure for stabilizer codes given by Gottesman and modify it to suit the setting of a class of non- CSS codes. Considering two types of noise models for this study, namely the depolarising noise and anisotropic noise, to depict the logical error rates obtained in decoding, we adopt the procedure of the bare ancilla method presented by Brown et al. to reorder the measurement sequence in the syndrome extraction step and upgrade it to obtain higher pseudo-thresholds and lower leading order terms of logical error rates.